Stochastic Streamflow Generation: A knn approach under a changing climate
Ze Jiang
2023-10-25
1 Setup
# this could remove the params
# rm(list=ls()); graphics.off() # clear environment and graphics
library(knitr)
#devtools::install_github(repo="haozhu233/kableExtra", ref="a6af5c0")
library(kableExtra)
library(rmarkdown)
# Global parameters
op <- par() # save original par
nensemble <- 100
flag.sel <- switch(2, "ALL","NPRED","WASP"); flag.sel## [1] "NPRED"flag.ver <- switch(1, "","_v1","_v2")
# Demo station
station_id <- "Q5"
#flag.save <- F
font_family <- "serif"
size_base <- 16
size_text <- 20
# Places the float at precisely the location in the pandoc code.
# Requires the float package. "H" is somewhat equivalent to "h!".
knitr::opts_chunk$set(echo = TRUE, include=TRUE, collapse = TRUE, comment = "#>",
message = FALSE, warning = FALSE,
#fig.path = paste0("figure/","-",flag.sel,flag.ver,"-"),
dev = "jpeg", dpi=500, out.width = '85%',
fig.height = 9, fig.width = 9,
fig.align='center', fig.pos="h!")2 Required packages
3 Load data
Observed streamflow (Q) and its conditional variables, Precipitation (P), Potential ET(PET), Temperature (T) as well as the water blance (P-PET).
# obsvered Q
data("Harz_obs_Q")
Qday_obs <- Harz_obs_Q[[station_id]] %>% rename("year"="iyear","month"="imon","day"="iday","Qd"="Qval")
Qmon_obs <- aggregate(Qd~year+month, Qday_obs, FUN = mean) %>% rename("Qm"="Qd") %>% arrange(year,month)
Qyr_obs <- stats::aggregate(Qd~year, Qday_obs, FUN = mean) %>% rename("Qa"="Qd") %>% arrange(year)
head(Qmon_obs[,1:2])
#> year month
#> 1 1925 11
#> 2 1925 12
#> 3 1926 1
#> 4 1926 2
#> 5 1926 3
#> 6 1926 4
tail(Qmon_obs[,1:2])
#> year month
#> 1137 2020 7
#> 1138 2020 8
#> 1139 2020 9
#> 1140 2020 10
#> 1141 2020 11
#> 1142 2020 12
date_Qobs <- as.Date(paste(Qmon_obs[,1],Qmon_obs[,2],"1", sep="-"))
range(date_Qobs)
#> [1] "1925-11-01" "2020-12-01"
# simulated monthly & daily
path.out <- paste0(station_id,"/")
load(paste0(path.out, "Harz_Qmon_",flag.sel,"_r",nensemble,"_hist",flag.ver,".Rdat")) # Qsim_mon
load(paste0(path.out, "Harz_Qday_",flag.sel,"_r",nensemble,"_hist",flag.ver,".Rdat")) # Qsim_day
summary(Qsim_mon[[1]])
#> year nn month Qm
#> Min. :1971 Min. :1929 Min. : 1.00 Min. :0.0295
#> 1st Qu.:1978 1st Qu.:1948 1st Qu.: 3.75 1st Qu.:0.1424
#> Median :1986 Median :1982 Median : 6.50 Median :0.2735
#> Mean :1986 Mean :1975 Mean : 6.50 Mean :0.3295
#> 3rd Qu.:1993 3rd Qu.:2002 3rd Qu.: 9.25 3rd Qu.:0.4582
#> Max. :2000 Max. :2020 Max. :12.00 Max. :1.5735
# merage
Qmon_obs1 <- Qmon_obs %>% rename("obs"="Qm")
Qmon_sim <- rbindlist(Qsim_mon, idcol="group") %>% rename("sim"="Qm") %>%
merge(Qmon_obs1, by=c("year","month")) %>%
mutate(season=cut(month, breaks=c(0, 3, 6, 9, 12), right = T, labels = c(1,2,3,4)))
# dates of hist ----
val.st <- 1971; val.end <- 2000
date_year <- val.st:val.end
date_year - unique(Qsim_mon[[1]]$year) #%>% range() # cross check
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
date_mon <- seq(as.Date(paste(val.st,"1","1",sep="-")),
as.Date(paste(val.end,"12","1",sep="-")),
by="month")
date_day <- seq(as.Date(paste(val.st,"1","1",sep="-")),
as.Date(paste(val.end,"12","31",sep="-")),
by="day")
ind_yrs <- which(unique(Qmon_obs[,1]) %in% date_year)
ind_mon <- which(date_Qobs %in% date_mon)
ind_day <- which(paste0(Qday_obs[,1], Qday_obs[,2], Qday_obs[,3]) %in%
paste0(year(date_day), month(date_day), day(date_day)))4 Monthly
4.1 Caculate statistics
#------------------------------------------------------------------------#
# OBS input
Qmon=Qmon_obs$Qm[ind_mon]
mon=Qmon_obs$mon[ind_mon]
year=Qmon_obs$year[ind_mon]
# SIM input
Qmon1 <- sapply(Qsim_mon, function(ls) ls$Qm)
#summary(Qmon1)
mon1=mon
year1=year
plot(date_mon, Qmon, type='l', col="white")
for(i_ens in 1:3){
lines(date_mon, Qmon1[,i_ens], col="grey")
}
lines(date_mon, Qmon, type='l', col="red")
nyr_obs <- val.end-val.st+1
nmo_obs <- nyr_obs*12
nyr_sim <- nyr_obs
nmo_sim <- nmo_obs
nrea <- nensemble
#------------------------------------------------------------------------#
# OBS initialisations
Qm <- numeric(length=12) # mean
Qs <- numeric(length=12) # stddev
Qmin <- numeric(length=12) # min
Qmax <- numeric(length=12) # max
Qsk <- numeric(length=12) # skewness
Qcor <- numeric(length=12) # lag-1 autocorrelation
Qacf_su <- numeric(length=20) # ACF summer 20 lags
Qacf_wi <- numeric(length=20) # ACF winter 20 lags
# SIM initialisations
Qm1 <- array(NA, dim=c(nrea,12)) # mean (dim: 'nrea' realisations, 12 months)
Qs1 <- array(NA, dim=c(nrea,12)) # stddev
Qmin1 <- array(NA, dim=c(nrea,12)) # min
Qmax1 <- array(NA, dim=c(nrea,12)) # max
Qsk1 <- array(NA, dim=c(nrea,12)) # skewness
Qcor1 <- array(NA, dim=c(nrea,12)) # lag-1 autocorrelation
Qacf1_su <- array(NA, dim=c(nrea,20)) # ACF summer 20 lags
Qacf1_wi <- array(NA, dim=c(nrea,20)) # ACF summer 20 lags
amin <- numeric(length=20) # min ACF 20 lags
amax <- numeric(length=20) # max ACF 20 lags
VDmax1 <- numeric(length=nrea) # max deficit volume (1)
DDmax1 <- numeric(length=nrea) # max deficit duration (2)
VSmax1 <- numeric(length=nrea) # max surplus volume (3)
DSmax1 <- numeric(length=nrea) # max surplus duration (4)
SM1 <- numeric(length=nrea) # storage capacity for full compensation (5)
LDP1 <- numeric(length=nrea) # longest dry period for full compensation (6)
Diff1 <- array(NA, dim=c(nyr_sim*12,nrea)) # mass curve cumsum(Q-MQ); 'nrea' realis;
sc <- array(NA, dim=c(nrea,6)) # storage characteristics (dim: 'nrea' realisations, 6 characteristics)
#------------------------------------------------------------------------#
# Basic OBS statistics by month
for (i in 1:12) {
Qm[i] <- mean(Qmon[mon == i])
Qs[i] <- sd(Qmon[mon == i])
Qmin[i] <- min(Qmon[mon == i])
Qmax[i] <- max(Qmon[mon == i])
Qsk[i] <- skewness(Qmon[mon == i])
}
# Basic SIM statistics by month for each realization
#summary(Qmon1)
for (i in 1:12) {
for (j in 1:nrea) {
Qm1[j,i] <- mean(Qmon1[,j][mon1 == i])
Qs1[j,i] <- sd(Qmon1[,j][mon1 == i])
Qmin1[j,i] <- min(Qmon1[,j][mon1 == i])
Qmax1[j,i] <- max(Qmon1[,j][mon1 == i])
Qsk1[j,i] <- skewness(Qmon1[,j][mon1 == i])
}
}
# Lag-1 autocorrelation per month for OBS & SIM
Qcor <- ac1mon(matrix(Qmon, ncol=12, byrow=T))
for (j in 1:nrea) { Qcor1[j,1:12]=ac1mon(matrix(Qmon1[,j], ncol=12,byrow=T))}
# ACF OBS & SIM 20 lags for summer and winter
Qacf_su <- acf(Qmon[mon>4 & mon<11], plot=FALSE)$acf[2:16] # OBS summer
Qacf_wi <- acf(Qmon[mon<5 | mon>10], plot=FALSE)$acf[2:16] # OBS winter
for(j in 1:nrea) { Qacf1_su[j,1:15] <- acf(Qmon1[,j][mon1>4 & mon1<11], plot=FALSE)$acf[2:16] } # SIM nreas summer
for(j in 1:nrea) { Qacf1_wi[j,1:15] <- acf(Qmon1[,j][mon1<5 | mon1>10], plot=FALSE)$acf[2:16] } # SIM nreas winter4.2 Basic statistics - monthly
#if(flag.save) jpeg("Qmon_valid.jpg", units="cm", width=16.5, height=22, res=dpi_fig)
# plot layout as matrix filled by cols
layout(matrix(c(1:10), nrow=5, ncol=2, byrow=TRUE))
par(ps="12", # size
las=1, # axis label orientation
mar=c(2,5,1,1), # no. of plot margin lines
oma=c(2,2,2,1), # no. of outer margin lines
mgp=c(2.5,0.5,0), # margin line for the axis title, labels and line.
pty="m") # maximum plot region used
# Box-Plot mean monthly Q
boxplot(Qm1, range=0, col = "lightblue", xlab='Month', ylab='Average [m3/s]') # grouped by month
points(Qm,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot StDev monthly Q
boxplot(Qs1, range=0, col = "lightblue", xlab='Month', ylab='Std. Dev. [m3/s]') # grouped by month
points(Qs,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Min monthly Q
boxplot(Qmin1, range=0, col = "lightblue", xlab='Month', ylab='Min [m3/s]') # grouped by month
points(Qmin,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Max monthly Q
boxplot(Qmax1, range=0, col = "lightblue", xlab='Month', ylab='Max [m3/s]') # grouped by month
points(Qmax,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Schiefe monthly Q
boxplot(Qsk1, range=0, col = "lightblue", xlab='Month', ylab='Schiefe [m3/s]') # grouped by month
points(Qsk,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Lag-1 autocorrelation monthly Q
boxplot(Qcor1, range=0, col = "lightblue", xlab='Month', ylab='Lag-1 Corr [-]') # grouped by month
points(Qcor,pch=4,col="red",lwd=2) # add obs mean value as red cross
abline(a=0, b=0, col="black",lty=2)
# Calculate storage statistics for OBS flows----------------------------------->
# (1,2) Maximum deficit volume (VDmax) and maximum deficit duration (DDmax) for Q < Qlow
VD <- 0.0; VDmax <- 0.0
DD <-0; DDmax <- 0
Qlow <- 0.5*mean(Qmon) # threshold
for (i in 1:nmo_obs) {
if (Qmon[i] < Qlow) {VD <- VD + (Qlow-Qmon[i]); DD <- DD+1}
else {VDmax <- max(VD,VDmax); VD <- 0; DDmax <- max(DD,DDmax); DD <- 0}
}
VDmax <- VDmax*2.628 # scale factor to obtain hm^3 from sum of m^3/s over several months (2.628*10^6 s/mon)
# (3,4) Maximum surplus volume (VSmax) and maximum surplus duration (DSmax) for Q > Qhigh
VS <- 0.0; VSmax <- 0.0
DS <-0; DSmax <- 0
Qhigh <- 2.0*mean(Qmon) # threshold
for (i in 1:nmo_obs) {
if (Qmon[i] > Qhigh) {VS <- VS + (Qmon[i]-Qhigh); DS <- DS+1}
else {VSmax <- max(VS,VSmax); VS <- 0; DSmax <- max(DS,DSmax); DS <- 0}
}
VSmax <- VSmax*2.628 # scale factor to obtain hm^3 from sum of m^3/s over several months (2.628*10^6 s/mon)
# (5,6) Storage capacity for total compensation of flows (SM) and longest dry period (LDP)
#Diff <- numeric(length=length(Qmon))
Diff <- cumsum(Qmon - mean(Qmon))
SM <- max(Diff)-min(Diff)
SM <- SM*2.628 # scale factor to obtain hm^3
LDP <- abs(which.max(Diff)-which.min(Diff)) # get index for max and min
# Calculate storage statistics for SIM flow------------------------------------>
# (1,2) Maximum deficit volume (VDmax1) and maximum deficit duration (DDmax1) for Q < Qlow
Qlow <- 0.5*mean(Qmon) # absolute threshold fixed from OBS !!!
for (j in 1:nrea) {
VD <- 0.0; VDmax1[j] <- 0.0
DD <-0; DDmax1[j] <- 0
for (i in 1:nmo_sim)
{
if (Qmon1[i,j] < Qlow) {VD <- VD + (Qlow-Qmon1[i,j]); DD <- DD+1}
else {VDmax1[j] <- max(VD,VDmax1[j]); VD <- 0; DDmax1[j] <- max(DD,DDmax1[j]); DD <- 0}
}
VDmax1[j] <- VDmax1[j]*2.628 # scale factor to obtain hm^3 from sum of m^3/s over several months (2.628*10^6 s/mon)
}
# (3,4) Maximum surplus volume (VSmax) and maximum surplus duration (DSmax) for Q > Qhigh
Qhigh <- 2.0*mean(Qmon) # absolute threshold fixed from OBS !!!
for (j in 1:nrea) {
VS <- 0.0; VSmax1[j] <- 0.0
DS <-0; DSmax1[j] <- 0
for (i in 1:nmo_sim)
{
if (Qmon1[i,j] > Qhigh) {VS <- VS + (Qmon1[i,j]-Qhigh); DS <- DS+1}
else {VSmax1[j] <- max(VS,VSmax1[j]); VS <- 0; DSmax1[j] <- max(DS,DSmax1[j]); DS <- 0}
}
VSmax1[j] <- VSmax1[j]*2.628 # scale factor to obtain hm^3 from sum of m^3/s over several months (2.628*10^6 s/mon)
}
# (5,6) Storage capacity for total compensation of flows (SM) and longest dry period (LDP)
for (j in 1:nrea) {
Diff1[,j] <- cumsum(Qmon1[,j] - mean(Qmon1[,j]))
SM1[j] <- max(Diff1[,j])-min(Diff1[,j])
SM1[j] <- SM1[j]*2.628 # scale factor to obtain hm^3
LDP1[j] <- abs(which.max(Diff1[,j])-which.min(Diff1[,j])) # get index for max and min
}
# Plot storage capacities
# Box-Plot StDev monthly Q
sc[,1] <- VDmax1/VDmax
sc[,2] <- DDmax1/DDmax
sc[,3] <- VSmax1/VSmax
sc[,4] <- DSmax1/DSmax
sc[,5] <- SM1/SM
sc[,6] <- LDP1/LDP
boxplot(sc, range=0, col = "lightblue", names=c('VD','DD','VS','DS','SM','LDP'), xlab = ' ', ylab='SIM/OBS [-]') # grouped by month
points(rep(1.0,6),pch=4,col="red",lwd=2) # add obs mean value as red cross
plot(Qacf_su, type='n', xlab='lag', ylab='ACF Summer [-]', ylim=c(-1.0,1.0), xlim=c(1,15))
#apply(Qacf1_su,1,lines,col='grey')
for(i in 1:nrow(Qacf1_su)) lines(Qacf1_su[i,],col='grey')
lines(Qacf_su,col='red',lwd=2)
lines(apply(Qacf1_su,2,mean),col='black',lwd=2,lty=2)
abline(a=0, b=0, col="black",lty=2)
plot(Qacf_wi, type='n', xlab='lag', ylab='ACF Winter [-]', ylim=c(-1.0,1.0), xlim=c(1,15))
#apply(Qacf1_wi,1,lines,col='grey')
for(i in 1:nrow(Qacf1_wi)) lines(Qacf1_wi[i,],col='grey')
lines(Qacf_wi,col='red',lwd=2)
lines(apply(Qacf1_wi,2,mean),col='black',lwd=2,lty=2)
abline(a=0, b=0, col="black",lty=2)
#if(flag.save) dev.off()
par(op)
4.3 IQR - monthly
# Calculate percentage of cases where OBS is covered by IQR of SIM
# over 6 statistics and 12 months (6*12)
Qmet_obs <- list(Qm, Qs, Qmin, Qmax, Qsk, Qcor)
Qmet_sim <- list(Qm1, Qs1, Qmin1, Qmax1, Qsk1, Qcor1)
n_met <- length(Qmet_obs)
theta1 <- 0.25; theta2 <- 0.75
theta3 <- 0.01; theta4 <- 0.99
IQR_cov <- 0
for(i in 1:12) {
for(j in 1:n_met) {
Q_tmp <- Qmet_obs[[j]]
Q_tmp1<- Qmet_sim[[j]]
if(Q_tmp[i] >= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] <= quantile(Q_tmp1[,i],theta2)) IQR_cov <- IQR_cov+1
if((Q_tmp[i] <= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] >= quantile(Q_tmp1[,i],theta3)) ||
(Q_tmp[i] <= quantile(Q_tmp1[,i],theta4) & Q_tmp[i] >= quantile(Q_tmp1[,i],theta2))) IQR_cov <- IQR_cov+0.5
#if(Q_tmp[i] >= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] <= quantile(Q_tmp1[,i],theta2)) IQR_cov <- IQR_cov+1
}
}
IQR_cov <- IQR_cov/(n_met*12)
print(paste0('IQR_cov=',round(IQR_cov,3)))
#> [1] "IQR_cov=0.667"4.4 Monthly Climatology
## monthly climatology
summary(Qsim_mon[[1]])
#> year nn month Qm
#> Min. :1971 Min. :1929 Min. : 1.00 Min. :0.0295
#> 1st Qu.:1978 1st Qu.:1948 1st Qu.: 3.75 1st Qu.:0.1424
#> Median :1986 Median :1982 Median : 6.50 Median :0.2735
#> Mean :1986 Mean :1975 Mean : 6.50 Mean :0.3295
#> 3rd Qu.:1993 3rd Qu.:2002 3rd Qu.: 9.25 3rd Qu.:0.4582
#> Max. :2000 Max. :2020 Max. :12.00 Max. :1.5735
summary(Qmon_obs)
#> year month Qm
#> Min. :1925 Min. : 1.000 Min. :0.0256
#> 1st Qu.:1949 1st Qu.: 4.000 1st Qu.:0.1283
#> Median :1973 Median : 7.000 Median :0.2673
#> Mean :1973 Mean : 6.509 Mean :0.3433
#> 3rd Qu.:1997 3rd Qu.:10.000 3rd Qu.:0.4606
#> Max. :2020 Max. :12.000 Max. :1.8729
#monthly average across years
x.mon.mean_r <- Qmon_sim[,.(sim=mean(sim), obs=mean(obs)),by=c("month","group")]
#summary(x.mon.mean_r)
x.mon.obs <- aggregate(Qm~month, Qmon_obs, FUN=mean)
#summary(x.mon.obs)
p.mon.clim1 <- ggplot(x.mon.mean_r,aes(x=factor(month), y=sim)) +
geom_boxplot() +
stat_summary(fun=mean, geom="point", shape=20, size=3, color="black") +
geom_point(data=x.mon.obs, aes(x=factor(month), y=Qm, color="Qobs_all"),shape=19) +
geom_point(data=x.mon.mean_r, aes(x=factor(month), y=obs, color="Qobs_val"),shape=17) +
scale_y_continuous(breaks = pretty_breaks()) +
scale_color_manual(values=c("red","blue")) +
labs(x="Month",y="Streamflow",title="Monthly Climatology",
color=NULL, fill=NULL) +
guides(fill="none") +
theme_bw() +
theme(text = element_text(size = 16,face='bold',family="serif"),
plot.margin = unit(c(0.1,0.1,0.1, 0.1), "cm"),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
# strip.background = element_blank(),
# strip.placement = "outside",
legend.position = "right",
#legend.position = c(.1,.85),
legend.direction = c("horizontal","vertical")[2],
legend.background = element_rect(fill="transparent"),
legend.title=element_blank()
)
p.mon.clim1 %>% print()
4.5 Seasonal Climatology
#average across years
x.ses.mean_r <- Qmon_sim[,.(sim=mean(sim), obs=mean(obs)),by=c("season","group")]
#summary(x.mon.mean_r)
p.sea.clim1 <- ggplot(x.ses.mean_r,aes(x=factor(season), y=sim)) +
geom_boxplot() +
stat_summary(fun=mean, geom="point", shape=20, size=3, color="black") +
geom_point(data=x.ses.mean_r, aes(x=factor(season), y=obs, color="Qobs"),shape=17) +
scale_y_continuous(breaks = pretty_breaks()) +
scale_color_manual(values="red") +
labs(x="Season",y="Streamflow",title="Seasonal Climatology",
color=NULL, fill=NULL) +
guides(fill="none") +
theme_bw() +
theme(text = element_text(size = 16,face='bold',family="serif"),
plot.margin = unit(c(0.1,0.1,0.1, 0.1), "cm"),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
# strip.background = element_blank(),
# strip.placement = "outside",
legend.position = "right",
#legend.position = c(.1,.85),
legend.direction = c("horizontal","vertical")[2],
legend.background = element_rect(fill="transparent"),
legend.title=element_blank()
)
p.sea.clim1 %>% print()
5 Yearly
5.1 Caculate statistics
#------------------------------------------------------------------------#
# OBS input
Qyr <- Qyr_obs$Qa[ind_yrs]
Qyr1 <- Qmon_sim[,.(value=mean(sim)),by=c("year","group")] %>% spread(group, value) %>%
dplyr::select(!c(year)) %>% as.matrix()
#summary(Qyr1)
#------------------------------------------------------------------------#
# OBS initialisations
Qm <- numeric(length=1) # mean
Qs <- numeric(length=1) # stddev
Qmin <- numeric(length=1)
Qmax <- numeric(length=1)
Qsk <- numeric(length=1) # skewness
Qacf <- numeric(length=15) # ACF 15 lags
# SIM initialisations
Qm1 <- numeric(length=nrea) # mean for each realisation
Qs1 <- numeric(length=nrea) # stddev
Qmin1 <- numeric(length=nrea) # min
Qmax1 <- numeric(length=nrea) # max
Qsk1 <- numeric(length=nrea) # skewness
Qacf1 <- array(NA, dim=c(nrea,15)) # ACF 15 lags
amin <- numeric(length=15) # min ACF 15 lags
amax <- numeric(length=15) # max ACF 15 lags
bpv <- array(NA, dim=c(nrea,4)) # array to hold box-plot-vars cs (dim: nreas, 4 vars)
#------------------------------------------------------------------------#
# Basic OBS statistics
Qm <- mean(Qyr)
Qs <- sd(Qyr)
Qmin <- min(Qyr)
Qmax <- max(Qyr)
Qsk <- skewness(Qyr) # req. package moments; method not clear !
# Basic SIM statistics for each realisation
for (j in 1:nrea) {
Qm1[j] <- mean(Qyr1[,j])
Qs1[j] <- sd(Qyr1[,j])
Qmin1[j] <- min(Qyr1[,j])
Qmax1[j] <- max(Qyr1[,j])
Qsk1[j] <- skewness(Qyr1[,j]) # req. package moments; method not clear !
}
# ACF OBS & SIM lags
Qacf <- acf(Qyr, plot=FALSE)$acf[2:16]
for(j in 1:nrea) { Qacf1[j,1:15] <- acf(Qyr1[,j], plot=FALSE)$acf[2:16]}5.2 Basic statistics - yearly
#if(flag.save) jpeg("Qyr_valid.jpg", units="cm", width=17, height=13, res=dpi_fig)
# plot layout as matrix filled by cols
layout(matrix(c(1:4), nrow=2, ncol=2, byrow=TRUE))
par(ps="12", # size
las=1, # axis label orientation
mar=c(2,5,1,2), # no. of plot margin lines
oma=c(2,2,2,1), # no. of outer margin lines
mgp=c(2.5,0.5,0), # margin line for the axis title, labels and line.
pty="m") # maximum plot region used
# Plot OBs annual TS
plot(Qyr, type='s',lwd=2,col='blue', xlab='Zeit [Jahre]', ylab='Qyr OBS [m3/s]') # plot annual time seris
abline(a=mean(Qyr), b=0, col="black",lty=2)
# Plot 1 realisation of SIM annual TS
plot(Qyr1[,1], type='s',lwd=2,col='blue', xlab='Zeit [Jahre]', ylab='Qyr SIM [m3/s]') # plot annual time seris
#line(Qyr1[,2], type='l', lwd=1, col='red')
abline(a=mean(Qyr1[,2]), b=0, col="black",lty=2)
# Combine variables for Box-Plot; build ratios SIM/OBS
bpv[,1] <- Qm1/Qm
bpv[,2] <- Qs1/Qs
bpv[,3] <- Qmin1/Qmin
bpv[,4] <- Qmax1/Qmax
#bpv[,5] <- Qsk1/Qsk
# Box-plot annual statistics
boxplot(bpv, range=0, col = "lightblue", names=c('mean','SD','min','max'),
xlab = ' ', ylab='SIM/OBS [-]') # grouped by month
points(rep(1.0,5),pch=4,col="red",lwd=2) # add obs mean value as red cross
# Plot ACF -- lines
plot(Qacf, type='n', xlab='lag', ylab='ACF [-]', ylim=c(-1.0,1.0), xlim=c(1,14))
for(i in 1:nrow(Qacf1)) lines(Qacf1[i,],col='grey')
lines(Qacf,col='red',lwd=2)
lines(apply(Qacf1,2,mean),col='black',lwd=2,lty=2)
6 Daily
6.1 Caculate statistics
#------------------------------------------------------------------------#
# OBS input
Qday <- Qday_obs$Qd[ind_day]
mon <- Qday_obs$mon[ind_day]
summary(Qday)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 0.0060 0.0940 0.2000 0.3456 0.4150 10.5000
# SIM input
Qday1 <- sapply(Qsim_day, function(ls) ls$Qd)
mon1 <- mon
#summary(Qday1)
#------------------------------------------------------------------------#
# OBS initialisations
Qm <- numeric(length=12) # mean
Qs <- numeric(length=12) # stddev
Qmin <- numeric(length=12)
Qmax <- numeric(length=12)
Qsk <- numeric(length=12) # skewness
Qcor <- numeric(length=12) # lag-1 autocorrelation
Qacf_su <- numeric(length=30) # ACF summer 30 lags
Qacf_wi <- numeric(length=30) # ACF winter 30 lags
# SIM initialisations
Qm1 <- array(NA, dim=c(nrea,12)) # mean (dim: nrea realisations, 12 months)
Qs1 <- array(NA, dim=c(nrea,12)) # stddev
Qmin1 <- array(NA, dim=c(nrea,12)) # min
Qmax1 <- array(NA, dim=c(nrea,12)) # max
Qsk1 <- array(NA, dim=c(nrea,12)) # skewness
Qcor1 <- array(NA, dim=c(nrea,12)) # lag-1 autocorrelation
Qacf1_su <- array(NA, dim=c(nrea,30)) # ACF summer 30 lags
Qacf1_wi <- array(NA, dim=c(nrea,30)) # ACF summer 30 lags
amin <- numeric(length=30) # min ACF 30 lags
amax <- numeric(length=30) # max ACF 30 lags
fmin <- numeric(length=nyr_sim*31) # min FDC by month
fmax <- numeric(length=nyr_sim*31) # max FDC by month
Qsrt1 <- array(NA, dim=c(nyr_sim*31,nrea)) # sorted Qday1 by month
#------------------------------------------------------------------------#
# Basic OBS statistics by month
for (i in 1:12) {
Qm[i] <- mean(Qday[mon == i])
Qs[i] <- sd(Qday[mon == i])
Qmin[i] <- min(Qday[mon == i])
Qmax[i] <- max(Qday[mon == i])
Qsk[i] <- skewness(Qday[mon == i]) # req. package moments; method not clear !
}
# Basic SIM statistics by month for each realization
for (i in 1:12) {
for (j in 1:nrea){
Qm1[j,i] <- mean(Qday1[,j][mon1 == i])
Qs1[j,i] <- sd(Qday1[,j][mon1 == i])
Qmin1[j,i] <- min(Qday1[,j][mon1 == i])
Qmax1[j,i] <- max(Qday1[,j][mon1 == i])
Qsk1[j,i] <- skewness(Qday1[,j][mon1 == i]) # req. package moments; method not clear !
}
}
# Lag-1 OBS autocorrelation per month
for (i in 1:12) {
Qcor[i] <- acf(Qday[mon == i], plot=FALSE, lag.max=1)$acf[2]
}
# Lag-1 SIM autocorrelation per month
for (i in 1:12) {
for (j in 1:nrea) {
Qcor1[j,i] <- acf(Qday1[,j][mon1 == i], plot=FALSE, lag.max=1)$acf[2]
}
}
# ACF OBS & SIM 30 lags for summer and winter
Qacf_su <- acf(Qday[mon>4 & mon<11], plot=FALSE)$acf[1:30] # OBS summer
Qacf_wi <- acf(Qday[mon<5 | mon>10], plot=FALSE)$acf[1:30] # OBS winter
for (j in 1:nrea) {
Qacf1_su[j,1:30] <- acf(Qday1[,j][mon1>4 & mon1<11], plot=FALSE)$acf[1:30]
}# SIM nrea reas summer
for (j in 1:nrea) {
Qacf1_wi[j,1:30] <- acf(Qday1[,j][mon1<5 | mon1>10], plot=FALSE)$acf[1:30]
} # SIM nrea reas winter6.2 Basic statistics - daily
#if(flag.save) jpeg("Qday1valid.jpg", units="cm", width=17, height=17, res=dpi_fig)
# plot layout as matrix filled by cols
layout(matrix(c(1:6), nrow=3, ncol=2, byrow=TRUE))
par(ps="12", # size
las=1, # axis label orientation
mar=c(2,5,1,2), # no. of plot margin lines
oma=c(2,2,2,1), # no. of outer margin lines
mgp=c(3,1,0), # margin line for the axis title, labels and line.
pty="m") # maximum plot region used
# Box-Plot mean daily Q
boxplot(Qm1, range=0, col = "lightblue", xlab='Month', ylab='Average [m3/s]') # grouped by month
points(Qm,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Std Dev daily Q
boxplot(Qs1, range=0, col = "lightblue", #ylim=c(0,100),
xlab='Month', ylab='Std. Dev. [m3/s]') # grouped by month
points(Qs,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Min daily Q
boxplot(Qmin1, range=0, col = "lightblue", #ylim=c(0,20),
xlab='Month', ylab='Min [m3/s]') # grouped by month
points(Qmin,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Max daily Q
boxplot(Qmax1, range=0, col = "lightblue", #ylim=c(0,2000),
xlab='Month', ylab='Max [m3/s]') # grouped by month
points(Qmax,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Schiefe daily Q
boxplot(Qsk1, range=0, col = "lightblue", #ylim=c(0,20),
xlab='Month', ylab='Schiefe [-]') # grouped by month
points(Qsk,pch=4,col="red",lwd=2) # add obs mean value as red cross
# Box-Plot Lag-1 autocorrelation daily Q
boxplot(Qcor1, range=0, col = "lightblue", #ylim=c(0.5,1),
xlab='Month', ylab='Lag-1 Corr [-]') # grouped by month
points(Qcor,pch=4,col="red",lwd=2) # add obs mean value as red cross
6.3 IQR - daily
# Calculate percentage of cases where OBS is covered by IQR of SIM
# over 6 statistics and 12 months (6*12)
Qmet_obs <- list(Qm, Qs, Qmin, Qmax, Qsk, Qcor)
Qmet_sim <- list(Qm1, Qs1, Qmin1, Qmax1, Qsk1, Qcor1)
n_met <- length(Qmet_obs)
theta1 <- 0.25; theta2 <- 0.75
theta3 <- 0.01; theta4 <- 0.99
IQR_cov <- 0
for(i in 1:12) {
for(j in 1:n_met) {
Q_tmp <- Qmet_obs[[j]]
Q_tmp1<- Qmet_sim[[j]]
if(Q_tmp[i] >= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] <= quantile(Q_tmp1[,i],theta2)) IQR_cov <- IQR_cov+1
if((Q_tmp[i] <= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] >= quantile(Q_tmp1[,i],theta3)) ||
(Q_tmp[i] <= quantile(Q_tmp1[,i],theta4) & Q_tmp[i] >= quantile(Q_tmp1[,i],theta2))) IQR_cov <- IQR_cov+0.5
#if(Q_tmp[i] >= quantile(Q_tmp1[,i],theta1) & Q_tmp[i] <= quantile(Q_tmp1[,i],theta2)) IQR_cov <- IQR_cov+1
}
}
IQR_cov <- IQR_cov/(n_met*12)
print(paste0('IQR_cov=',round(IQR_cov,3)))
#> [1] "IQR_cov=0.694"6.4 CDF
# plot summer & winter ACF and FDC for 4 selected months as 3 x 2 matrix
#if(flag.save) jpeg("Qday2valid.jpg", units="cm", width=17, height=17, res=400)
# plot layout as matrix filled by cols
layout(matrix(c(1:6), nrow=3, ncol=2, byrow=TRUE))
par(ps="12", # size
las=1, # axis label orientation
mar=c(2,5,1,2), # no. of plot margin lines
oma=c(2,2,2,1), # no. of outer margin lines
mgp=c(3,1,0), # margin line for the axis title, labels and line.
pty="m") # maximum plot region used
# Plot daily ACF summer - polygon
x <- c(1:30)
xx <- c(x,rev(x)) # x-values for polygon
for (k in 1:30) {
amin[k] <- min(Qacf1_su[,k])
amax[k] <- max(Qacf1_su[,k])
}
yy <- c(amin,rev(amax)) # y-values for polygon
plot(Qacf_su, type='l', ylim=c(0,1), xlab='lag', ylab='ACF Summer [-]')
polygon(xx,yy,col="lightgrey",border=NA)
lines(Qacf_su, type='l')
# Plot daily ACF winter - polygon
x <- c(1:30)
xx <- c(x,rev(x)) # x-values for polygon
for (k in 1:30) {
amin[k] <- min(Qacf1_wi[,k])
amax[k] <- max(Qacf1_wi[,k])
}
yy <- c(amin,rev(amax)) # y-values for polygon
plot(Qacf_wi, type='l', ylim=c(0,1), xlab='lag', ylab='ACF Winter [-]')
polygon(xx,yy,col="lightgrey",border=NA)
if(nensemble==1) lines(xx,yy,col="red",border=NA)
lines(Qacf_wi, type='l')
# Calculate and plot flow duration curve by month OBS & SIM
ystr<-c('Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec')
# months January, April, July, October
for (m in seq(1,12,by=3)) {
Qsrt <- sort(Qday[mon==m])
n0 <- length(Qday[mon==m])
Fn <- seq(1,n0)/(n0+1)
n1 <- length(Qday1[,1][mon1==m])
for (j in 1:nrea) { Qsrt1[1:n1,j] <- sort(Qday1[,j][mon1==m]) }
Fn1 <- seq(1, n1)/(n1+1)
xx <- c(Fn1,rev(Fn1))
for (k in 1:n1)
{
fmin[k] <- min(Qsrt1[k,])
fmax[k] <- max(Qsrt1[k,])
}
yy <- c(fmin[1:n1],rev(fmax[1:n1])) # y-values for polygon
plot(Fn, Qsrt, type='l', pch=1, cex=0.5, log="y", #ylim=c(1,500),
xlab='Pu [-]', ylab=paste('Q [m3/s] - ',ystr[m]))
polygon(xx,yy,col="lightgrey",border=NA)
lines(Fn,Qsrt, type='l', pch=1, cex=0.5)
}
7 Seasonality change
out.Qmon <- list()
gcms <- c("hist","rcp85_near", "rcp85_far")
for(i in 1:length(gcms)) {
flag.gcm <- gcms[i]
print(flag.gcm)
Qsim_mon <- get(load(paste0(path.out, "Harz_Qmon_",flag.sel,"_r",nensemble,"_",flag.gcm,flag.ver,".Rdat")))
out.Qmon[[i]] <- rbindlist(Qsim_mon, idcol="group") %>% data.frame()
}
#> [1] "hist"
#> [1] "rcp85_near"
#> [1] "rcp85_far"
names(out.Qmon) <- gcms
summary(out.Qmon[[3]])
#> group year nn month
#> Min. : 1.00 Min. :2071 Min. :1926 Min. : 1.00
#> 1st Qu.: 25.75 1st Qu.:2078 1st Qu.:1951 1st Qu.: 3.75
#> Median : 50.50 Median :2086 Median :1975 Median : 6.50
#> Mean : 50.50 Mean :2086 Mean :1975 Mean : 6.50
#> 3rd Qu.: 75.25 3rd Qu.:2093 3rd Qu.:2000 3rd Qu.: 9.25
#> Max. :100.00 Max. :2100 Max. :2020 Max. :12.00
#> Qm
#> Min. :0.02073
#> 1st Qu.:0.11524
#> Median :0.23472
#> Mean :0.30635
#> 3rd Qu.:0.41928
#> Max. :1.94281
x.mon.mean_r <- rbindlist(out.Qmon, idcol="gcm") %>% rename("sim"="Qm")
x.mon.mean_r$gcm <- factor(x.mon.mean_r$gcm)
x.mon.mean_r$gcm <- factor(x.mon.mean_r$gcm, levels=gcms)
summary(x.mon.mean_r)
#> gcm group year nn
#> hist :36000 Min. : 1.00 Min. :1971 Min. :1926
#> rcp85_near:36000 1st Qu.: 25.75 1st Qu.:1993 1st Qu.:1947
#> rcp85_far :36000 Median : 50.50 Median :2036 Median :1973
#> Mean : 50.50 Mean :2036 Mean :1972
#> 3rd Qu.: 75.25 3rd Qu.:2078 3rd Qu.:1997
#> Max. :100.00 Max. :2100 Max. :2020
#> month sim
#> Min. : 1.00 Min. :0.01712
#> 1st Qu.: 3.75 1st Qu.:0.12572
#> Median : 6.50 Median :0.25861
#> Mean : 6.50 Mean :0.32848
#> 3rd Qu.: 9.25 3rd Qu.:0.44907
#> Max. :12.00 Max. :1.96039
#monthly average across years
x.mon.mean_r1 <- x.mon.mean_r[,.(sim=mean(sim)),by=c("month","group","gcm")]
summary(x.mon.mean_r1)
#> month group gcm sim
#> Min. : 1.00 Min. : 1.00 hist :1200 Min. :0.0886
#> 1st Qu.: 3.75 1st Qu.: 25.75 rcp85_near:1200 1st Qu.:0.2069
#> Median : 6.50 Median : 50.50 rcp85_far :1200 Median :0.3011
#> Mean : 6.50 Mean : 50.50 Mean :0.3285
#> 3rd Qu.: 9.25 3rd Qu.: 75.25 3rd Qu.:0.4492
#> Max. :12.00 Max. :100.00 Max. :0.6920
p.mon.clim1 <- ggplot(x.mon.mean_r1, aes(x=factor(month), y=sim, fill=gcm)) +
geom_boxplot() +
#stat_boxplot(geom ='errorbar')+
#stat_summary(fun=mean, geom="point", shape=20, size=3, color="black") +
scale_y_continuous(breaks = pretty_breaks()) +
scale_fill_manual(values=c("grey","blue","red")) +
labs(x="Month",y="Qmon[m3/s]",#title="Monthly Climatology",
color=NULL, fill=NULL) +
#guides(fill="none") +
theme_bw() +
theme(text = element_text(size = 16,face='bold',family="serif"),
plot.margin = unit(c(0.1,0.1,0.1, 0.1), "cm"),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
# strip.background = element_blank(),
# strip.placement = "outside",
#legend.position = "right",
legend.position = c(.6,.9),
legend.direction = c("horizontal","vertical")[1],
legend.background = element_rect(fill="transparent"),
legend.title=element_blank()
)
p.mon.clim1 %>% print()
8 Storage change
# Calculate storage statistics for current flows----------------------------------->
# (1,2) Maximum deficit volume (VDmax) and maximum deficit duration (DDmax) for Q < Qlow
Qmon <- Qmon_obs$Qm[ind_mon]
Qsim_mon <- out.Qmon[[1]]
summary(Qmon)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 0.0256 0.1268 0.2701 0.3457 0.4698 1.8729
Qmon1 <- dplyr::select(Qsim_mon,!nn) %>% spread(group, Qm) %>% dplyr::select(!c(year,month)) %>%
as.matrix()
s.hist <- storage(Qmon, Qmon1)
out.storage <- list()
for(i_gcm in 2:length(gcms)) {
flag.gcm <- gcms[i_gcm]
print(flag.gcm)
Qsim_mon <- out.Qmon[[i_gcm]]
#summary(Qmon)
Qmon1 <- dplyr::select(Qsim_mon,!nn) %>% spread(group, Qm) %>% dplyr::select(!c(year,month)) %>%
as.matrix()
sc <- array(NA, dim=c(nrea,6)) # storage characteristics (dim: 'nrea' realisations, 6 characteristics)
# Calculate storage statistics for SIM flow------------------------------------>
s.gcm <- storage(Qmon, Qmon1)
VDmax1 <- s.gcm$VD
DDmax1 <- s.gcm$DD
VSmax1 <- s.gcm$VS
DSmax1 <- s.gcm$DS
SM1<- s.gcm$SM
LDP1 <- s.gcm$LDP
# Plot storage capacities
# Box-Plot StDev monthly Q
sc[,1] <- VDmax1/s.hist$VD
sc[,2] <- DDmax1/s.hist$DD
sc[,3] <- VSmax1/s.hist$VS
sc[,4] <- DSmax1/s.hist$DS
sc[,5] <- SM1/s.hist$SM
sc[,6] <- LDP1/s.hist$LDP
sc.df <- data.frame(sc)
colnames(sc.df) <- c("VD","DD","VS","DS","SM","LDP")
out.storage[[i_gcm]] <- sc.df
}
#> [1] "rcp85_near"
#> [1] "rcp85_far"
names(out.storage) <- gcms
sc.plot <- rbindlist(out.storage,idcol="gcm")
sc.plot$gcm <- factor(sc.plot$gcm)
sc.plot$gcm <- factor(sc.plot$gcm, levels=gcms)
#summary(sc.plot)
sc.plot1 <- sc.plot %>% gather(group,sc,2:7)
sc.plot1$group <- factor(sc.plot1$group)
sc.plot1$group <- factor(sc.plot1$group, levels= c("VD","DD","VS","DS","SM","LDP"))
summary(sc.plot1)
#> gcm group sc
#> hist : 0 VD :200 Min. :0.1452
#> rcp85_near:600 DD :200 1st Qu.:0.8020
#> rcp85_far :600 VS :200 Median :1.0011
#> DS :200 Mean :1.0603
#> SM :200 3rd Qu.:1.2971
#> LDP:200 Max. :2.8800
p.sc <- ggplot(subset(sc.plot1,gcm!="hist"), aes(x=group, y=sc, color=gcm)) +
geom_boxplot(position = position_dodge(width = 1)) +
#stat_boxplot(geom ='errorbar')+
stat_summary(fun=mean, geom="point", shape=17, size=5,position = position_dodge(width = 1)) +
geom_abline(slope=0,intercept=1, color="black") +
scale_y_continuous(limits=c(0,2), breaks = pretty_breaks()) +
scale_color_manual(values=c("grey","blue","red")[2:3]) +
labs(x="Storage characteristics",y="Future/Past[-]",
color=NULL, fill=NULL) +
theme_bw() +
theme(text = element_text(size = 16,face='bold',family="serif"),
plot.margin = unit(c(0.1,0.1,0.1, 0.1), "cm"),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
# strip.background = element_blank(),
# strip.placement = "outside",
#legend.position = "right",
legend.position = c(.2,.9),
legend.direction = c("horizontal","vertical")[1],
legend.background = element_rect(fill="transparent"),
legend.title=element_blank()
)
p.sc